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arXiv:cond-mat/9812251

U(1)XSU(2) Gauge theory of underdoped high Tc cuprates via Chern-Simons bosonization

P. A. Marchetti

Published Dec 15, 1998• 0 citations
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Abstract

We outline the basic ideas involved in a recently proposed derivation of a gauge theory for underdoped cuprates in the "spin-gap phase", performed essentially step by step starting from the t-J model, considered as a model Hamiltonian for the CuO_2 layers. The basic tool is the U(1)XSU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a "spin-gap" not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (π/2, π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.

DOI
10.48550/arxiv.cond-mat/9812251

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We outline the basic ideas involved in a recently proposed derivation of a gauge theory for underdoped cuprates in the "spin-gap phase", performed essentially step by step starting from the t-J model, considered as a model Hamiltonian for the CuO_2 layers. The basic tool is the U(1)XSU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a "spin-gap" not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (π/2, π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.
We outline the basic ideas involved in a recently proposed [17] derivation of a gauge theory for underdoped cuprates in the “spin gap phase”, performed essentially step by step starting from the t — J model, considered as a model Hamiltonian for the CuO2 layers. The basic tool is the U(1) x SU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a “spingap” not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (±π/2, ±π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.
The Chern-Simons bosonization with $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ gauge field is applied to the two-dimensional $t\ensuremath{-}J$ model in the limit $t\ensuremath{\gg}J,$ to study the normal-state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average---a coexisting flux phase and s+ids+ids+id-like resonating-valence-bond state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field VVV, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a \ensuremath{\pi} flux phase for the holons, converting them into Dirac-like fermions, while the VVV field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero-doping limit. The nonlinear-\ensuremath{\sigma} model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long-range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi-liquid theory with a Fermi surface consisting of four ``half-pockets'' centered at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) and one reproduces the results for the electron spectral function obtained in the mean-field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalization effects due to gauge fluctuations give rise to non-Fermi-liquid behavior for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors (mainly due to the short-ranged AF order) and predicts that the minimal gap for the physical electron is proportional to the square root of the doping concentration. Therefore the gap does not vanish in any direction. All these predictions can be checked explicitly in experiment.
The U(1)×SU(2) Chern–Simons gauge theory is applied to study the 2D t–J model describing the normal state of underdoped cuprate superconductors. The U(1) field produces a flux phase for holons converting them into Dirac-like fermions, while the SU(2) field, due to the coupling to holons gives rise to a gap for spinons. An effective low-energy action involving holons, spinons and a self-generated U(1) gauge field is derived. The Fermi surface and electron spectral function obtained are consistent with photoemission experiments. The theory predicts a minimal gap proportional to doping concentration. It also explains anomalous transport properties.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
We propose an explanation of several experimental features related to the "pseudogap" in high Tc cuprates in terms of a spin-charge gauge theory. In this approach, based on a formal spin-charge separation applied to the t-J model, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap ms~J(δ| ln δ|)1/2, where δ is the doping concentration) and holons with "small" Fermi surface (∊F~tδ) interacting via a gauge field. The main effect of gauge fluctuations is to introduce a dissipation ~T/χ, where χ is the diamagnetic susceptibility. The competition between the two energy scales, ms and T/χ, is the root in our approach of many phenomena peculiar to in-plane transport properties of the "pseudogap phase". Furthermore the gauge interaction induces binding of spinon and holon into an "electron" resonance. This binding introduces another energy scale, the recombination rate, which dominates the out-of-plane resistivity, yielding an insulating behavior. A good agreement is found between the experimental data and theoretically derived doping and temperature dependence of resistivity, both in-plane and out-of-plane, and spin relaxation.